Abstract
Solid oxide fuel cells (SOFCs) are recognized as a clean energy source that, unlike internal combustion engines, produces no CO2 during operation when H2 is used as a fuel. They use a highly efficient chemical-to-electrical energy conversion process to convert oxygen and hydrogen into electricity and water. They can provide smaller-scale power for transportation (e.g., cars, buses, and ships) and be scaled up to provide long-term energy for an electrical grid, making SOFCs a promising, clean alternative to hydrocarbon combustion. Conventional SOFCs faced challenges of high operating temperatures, high cost, and poor durability. Research into advanced cathode, anode, electrolyte, and interconnect materials is providing more insight into the ideal structural and chemical properties that enable the commercialization of highly stable and efficient intermediate temperature (IT) SOFCs. In this paper, we discuss the functional properties of the cathode, anode, electrolyte, and interconnectors for IT-SOFCs. The performance of SOFCs depends not only on the materials used but also on the optimization of operating conditions to maximize efficiency. The voltaic, thermodynamic, and fuel efficiency of SOFCs is presented.
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Introduction
To meet global energy demands, while achieving net-zero emissions by 2050, it is essential to advance environmentally sustainable alternatives to the combustion of fossil fuels [1]. Solid oxide fuel cells (SOFCs) are a promising alternative that uses a highly efficient chemical-to-electrical energy conversion process to convert oxygen and hydrogen into electricity and water (Fig. 1) [2]. Compared to other fuel cells, such as proton exchange membrane, alkaline, or direct methanol fuel cells, SOFCs can achieve the highest efficiency and power output [3]. Despite the efficiency of SOFCs, they have yet to see widespread distribution due to the high cost of manufacturing and poor durability. Recent focus has been on developing alternative cathode, electrolyte, and anode materials that can operate at intermediate temperatures (IT) (600–800 °C) to allow for the use of cheaper interconnect materials and improve the durability [4]. Here, we discuss the recent development of cathodes, electrolytes, anodes, and interconnects for IT SOFCs, as well as the chemical and physical requirements. Furthermore, the thermodynamic, fuel, and voltaic efficiency of SOFCs for optimal cell performance is suggested.
Solid oxide fuel cell components
Cathodes
Cathode materials for SOFCs are designed to meet the following functional properties. (i) High catalytic activity towards the oxygen reduction reaction (ORR) at intermediate temperatures (IT) (600–800 °C). The ORR is a multistep reaction involving oxygen diffusion, adsorption, dissociation, diffusion towards the catalytically active triple-phase-boundary (TPB), electron transfer, and ion transfer to the electrolyte (Fig. 2) [5]. For a material to have high catalytic activity towards the ORR, it must have low resistance for each step of the ORR; the total resistance for the ORR should be less than 0.1 Ω cm2 at an IT for high-performance SOFCs. This is experimentally determined using electrochemical impedance spectroscopy (EIS); the total resistance can be deconvoluted into the individual steps of the ORR using a distribution function of relaxation times (DRT) and equivalent circuit modeling [6,7,8].
(ii) High total electrical conductivity (mixed ionic and electronic conductivity (MIEC)) (> 100 S/cm at ITs in air/O2) to improve the electron charge transfer kinetics of the ORR and to extend the TPB. The conductivity of an SOFC cathode is measured using a 2 or 4-probe DC or AC technique [9]. By using a ionic conducting probe such as Sm-doped CeO2 and Y-doped ZrO2 (electron-blocking electrode), the ionic conductivity of the cathode can be isolated [10]. In contrast, by using a purely electronic conducting probe such as dense Pt (ion-blocked), the electronic conductivity of the material can be isolated [11]. Interface compatibility should be considered carefully, and measurements should be performed using different sample dimensions to ensure reproducibility. (iii) Compatibility with the electrolyte and interconnect materials including chemical stability and a matching thermal expansion coefficient (TEC). The chemical stability can be determined using X-ray diffraction (XRD), scanning electron microscopy (SEM), and elemental mapping (EDS) of the samples before and after high-temperature exposure to the electrolyte [7, 12]. The TEC is determined by measuring the samples displacement (either length or volume) as a function of temperature; the acceptable limit for a TEC mismatch between the cathode and electrolyte/interconnects is ~ 15–20% to avoid cell cracking and cathode delamination [13]. (iv) Structural stability under SOFC operating conditions (IT, oxidizing environment, dual-atmosphere, and polarization). The chemical stability of SOFC components can be determined using microscopy and spectroscopy methods before and after operating [14]. EIS of the SOFC during operation and analyzing how the spectrum changes with time using DRT gives insight into how the structural changes are affecting the ORR mechanism [15,16,17]. For example, an increase in the high-frequency impedance (charge transfer resistance) may indicate reactivity between the cathode and electrolyte [18]. SOFC cathodes that can meet these criteria include perovskites, layered perovskites, double perovskites, and Ruddlesden-Popper phase materials (Fig. 3 and Table 1) [6,7,8, 19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34].
Perovskite-type cathodes
Perovskites are materials that share the same crystal structure as the mineral CaTiO3 giving them the general chemical formula of ABO3; the larger size atom sits at the 12-coordinate A-site while the smaller size atom sits at the 6-coordinate B-site (Fig. 3) [35]. The structure is formed by connecting BO6 octahedrons with the A-ion occupying the space between the octahedrons [36]. Doping lower oxidation state ions into the A and B site introduces oxygen vacancies which improve the kinetics of the last step of the ORR (Fig. 2) [37, 38]. If the cathode is a mixed ionic and electronic conductors (MIECs), this step can occur at the cathode-oxygen interface; for purely electronic conducting cathodes, this step can only occur at the TPB [39]. Lanthanum strontium manganite (LSM) has been extensively studied owing to its high stability and catalytic activity towards the ORR at elevated temperatures (< 0.1 Ω cm2 at 800 °C) [2, 40]. However, at ITs, the resistance at the LSM becomes far to large (> 10 Ω cm2 at 650 °C) to be useful in SOFCs operating at ITs [41]. LSM also has negligible ionic conductivity (< 6 × 10−7 S/cm) reducing the active area for ORR [42]. Lanthanum strontium cobalt ferrite (LSCF) is one of the most popular cathodes for IT SOFCs due to its MIEC properties, high electrical conductivity (> 300 S/cm at 700 °C), and ORR catalytic activity (< 0.1 Ω cm2 at 700 °C) (Fig. 4) [25, 43]. However, LSCF has been shown to become poisoned by Cr-containing interconnects and experiences Sr segregation during SOFC operating conditions (Fig. 5) [44,45,46].
Layered perovskite-type cathodes
Layered perovskites are described by the general chemical formula AA’B2O5+δ with A being lanthanides or yttrium; A’ being Ba or Sr; and B being Co, Fe, or Mn (Fig. 3) [47]. Their structure has ordered A-site cations where the A and A’ layers alternate along the (001) plane and oxygen vacancies appear in the A layer [47, 48]. Interest in these materials as potential cathodes for SOFCs is owed to their low TECs and high MIEC with a more stable B site when compared to disordered perovskites [49]. Among the layered perovskites, GdBaCo2O5+δ (GBCO) shows a total conductivity of 100–1000 S/cm, ionic conductivity of 0.01 S/cm, and ORR catalytic activity of 0.1 Ω cm2 at 700 °C (Fig. 6) [30, 31, 50]. However, GBCO has shown to be highly reactive with yttrium-stabilized zirconia (YSZ) electrolyte as well as forming secondary phases with La0.8Sr0.2Ga0.8Mg0.2O3−δ (LSGM) and Ce0.9Gd0.1O1.95 (CGO) electrolytes which may reduce the cells performance with time (Fig. 7) [51]. Further research still needs to be done to determine the structural stability of layered perovskite-type cathodes under working SOFC conditions [51, 52].
Double-perovskite-type cathodes
Double perovskites are described by the general chemical formula A2BB’O6−δ or AA’BB’O6−δ where alkali, alkaline earth, or rare earth ions sit at the A and A’ site and metal ions sit at the B and B’ site (Fig. 3) [36]. Their structure is similar to that of a single perovskite with BO6 and B’O6 octahedrons where A and A’ occupy the space between the octahedrons [36]. These materials are interesting candidates for SOFC cathodes due to their ability to hold high oxygen vacancies and stabilize multivalent ions through doping which increases the electronic conductivity [33, 53]. Ba2CoMo0.5Nb0.5O6−δ (BCMN) was found to have high catalytic activity towards the ORR (0.1 Ω/cm2 at 700 °C), structural stability at ITs (240 h at 750 °C), and no reactivity with the Sm-doped CeO2 (SDC) electrolyte [33]. However, the electrical conductivity is very low (1 S/cm at 700 °C) caused by the large separation between multivalent Co-ions (Fig. 8). The separation between the electronically active ions causes low conductivity in other double perovskite cathodes [54,55,56].
Anodes
Anode materials for IT SOFCs are designed to meet the following properties. (i) High catalytic activity towards the hydrogen oxidation reaction (HOR). Similar to ORR, the HOR is also a multistep reaction involving hydrogen diffusion, adsorption, oxidation at the TPB, adsorption of OH− onto the ion conductor’s surface, second oxidation at the TPB, and release of water vapor (Fig. 9) [57]. For a material to have high catalytic activity towards the HOR, it must have low resistance for each step of the HOR; the total resistance for the HOR should be < 0.5 Ω cm2 at an IT in H2 [58,59,60]. (ii) High total conductivity (> 100 S/cm) at ITs in an H2 environment to improve the electron charge transfer kinetics of the HOR and extend the TPB [61]. (iii) Compatibility with the electrolyte and interconnect materials. (iv) Structural stability under SOFC operating conditions (IT, reducing environment, dual-atmosphere, and polarization). Classes of materials for SOFC anodes that can meet these criteria include Ni-cermet, perovskite-type, and Cu-based anodes (Table 2) [62,63,64,65,66,67,68,69,70,71,72].
Ni-cermet anodes
Ni is a good candidate as an anode material for SOFCs owing to its low cost, high catalytic activity towards the HOR, and high conductivity [73]. However, poor adherence to ceramic electrolytes, structural instability, and no ionic conductivity prevent its use [61]. By creating a composite of Ni and a ceramic electrolyte (Ni-cermet), all three of these problems can be circumvented (Fig. 10) [74, 75]. An anode with 50 wt% NiO (reduces to Ni upon exposure to H2) and 50 wt% YSZ has high catalytic activity towards the HOR (0.2 Ω cm2 at 800 °C), high electrical conductivity (> 1000 S/cm at 800 °C), and the YSZ creates ion conducting networks (Fig. 11) [62, 63].
At elevated temperatures (> 555 °C) and in the presence of moist hydrogen (> 1% H2O), Ni metal will be volatilized into Ni(OH)2(g), evaporate inside the anode, and precipitate on the surface [76, 77]. Thus, long-term stability remains a problem for Ni-cermet anodes due to the depletion of nickel metal at the TPB and agglomeration of nickel particles reducing the active area (Fig. 12) [78].
Perovskite-type anodes
Several known perovskite-type oxides are unviable for SOFC anodes due to low catalytic activity towards the HOR, low conductivity, and instability in reducing environments, as they readily form oxide ion vacancies [79, 80]. The La0.5Sr1.5MnO4+δ (L5S15M) Ruddleson-Popper was screened as a potential candidate as an SOFC cathode but its catalytic activity towards the HOR (0.61 Ω cm2 at 800 °C) is too low to replace the typical Ni metal anode (Fig. 13) [81].
The La0.5Sr0.5Fe0.8Ni0.1Nb0.1O3−δ (LSCFNN) perovskite has been demonstrated in a full SOFC using a Sc-doped ZrO2 (ScSZ) electrolyte and a La0.5Sr0.5Fe0.8Cu0.15Nb0.05O3−δ (LSFCN) cathode showing a low resistance (0.15 Ω cm2 at 800 °C, wet H2 fuel, air oxidant) and stability at 0.7 V for 50 h (Fig. 14) [82]. Symmetric cell testing should be done on La0.5Sr0.5Fe0.8Ni0.1Nb0.1O3−δ to isolate for the anode performance.
The Sr2CrMoO6−δ double-perovskite has higher electrical conductivity (92 S/cm at 800 °C in 5% H2) when compared to other Sr and Cr containing perovskite anodes such as La0.75Sr0.25Cr0.5Mn0.5O3−δ (0.95 S/cm at 800 °C in 5% H2). This is attributed to the high concentration of Mo6+ and Cr2+ in the crystal structure which conduct electrons through the Mo5+/Mo6+ redox couple and Mo6+—Cr2+ double exchange interactions [68, 72]. It is also tolerant to H2S impurities in fuel which damage typical Ni-cermet anodes; however, the resistance towards the HOR is four times higher (0.71 Ω cm2 at 800 °C in H2) than typical Ni-cermet anodes limiting the total power capabilities [72].
Cu-cermet anodes
Cu-cermet anodes are typically used over Ni-cermet anodes in SOFCs utilizing hydrocarbons as fuel due to minimal coking at the anode surface [83]. However, Cu itself is not active for the HOR so ceria is added as the catalyst, copper provides the electronic conductivity (> 70 S/cm at 700 °C), and an ion conductor is added [83, 84]. When using H2 as fuel, Cu–CeO2–YSZ anodes show comparable activity towards the HOR (< 0.5 Ω cm2 at IT) as Ni-YSZ; when using CO as fuel, Cu-CeO2-YSZ shows ~ 3 × the performance when compared to Ni-YSZ [64, 85]. Thus, Cu–CeO2–YSZ is a good candidate for SOFCs operating in either hydrocarbons or hydrogen containing impurities. Other Cu-cermet anodes have shown copper migration and agglomeration so the long-term stability of these materials under SOFC conditions should be determined [86].
Oxide ion electrolytes
Electrolyte materials for SOFCs are designed to meet the following criteria. (i) High oxide ion conductivity (> 0.1 S/cm at IT) to minimize the ohmic resistance with minimal electronic conductivity [87]. Ions are conducted via a vacancy hopping mechanism so a higher concentration of oxygen vacancies improves the ionic conductivity (Eq. 1 and Fig. 15) [88,89,90].
(ii) Structural stability under SOFC operating conditions (IT, oxidizing and reducing environment, dual-atmosphere, and polarization). It must form a dense structure to avoid gas diffusion through the electrolyte; and (iii) compatibility with the electrode and interconnect materials including chemical stability and a TEC match. Classes of materials for SOFC electrolytes that can meet the above criteria include fluorite-type, perovskite-type, and apatite-type electrolytes (Fig. 16 and Table 3) [91,92,93,94,95,96,97,98].
Fluorite-type electrolytes
The fluorite structure is described by the chemical formula of AO2 where the cation sits at the 4-coordinate A-site located at the face and edge positions while oxygen sits at the interstitial sites (Fig. 16) [100]. ZrO2 is a good oxide-ion conductor when in the cubic fluorite phase, however, it only maintains this structure at temperatures above 2300 °C; upon quenching below 2300 °C, the cubic-fluorite structure decomposed into the poor oxide-ion conducting hexagonal structure [101, 102]. By doping Y2O3, the cubic ZrO2 structure is stabilized at low temperatures, and oxygen vacancies are introduced (Eq. 2 and Fig. 17) [103].
Yttria stabilized zirconia (YSZ) has high ionic conductivity of 0.1 S/cm at 1000 °C but at ITs, the ionic conductivity is low (> 0.02 S/cm at 800 °C) making it impractical for IT-SOFCs (Fig. 18) [94, 96]. The cubic YSZ structure has also been shown to decompose during SOFC operating conditions which will lower the ionic conductivity with time [104].
Unlike ZrO2, CeO2 maintains the cubic fluorite structure at all temperatures but pure CeO2 is a mixed conductor and is reduced by H2 to give electronic conducting species making it unsuitable as an electrolyte [105]. Doping CeO2 with rare earth elements greatly raises the ionic conductivity and stabilizes CeO2 in reducing environments; samarium-doped ceria has an ionic conductivity that is an order of magnitude larger than YSZ and is the most stable in reducing atmospheres when compared to the other rare earth-doped CeO2 electrolytes (Fig. 19) [91].
Perovskite-type electrolytes
Perovskite-type structures as electrolytes for SOFC are appealing due to their high ionic conductivity and oxygen-deficient structure allowing for oxide ion vacancy hopping [106]. La1−xSrxGa1−yMgyO3−δ (LSGM) type materials are very popular as SOFC electrolytes [107, 108]. LSGM has an ionic conductivity of ~ 0.1 S/cm at 800 °C (with negligible electronic conductivity) which is comparable to YSZ at 1000 °C (Fig. 20) [109].
The lower operating temperature of LSGM makes it an appealing choice for IT-SOFC. However, synthesis of a single LSGM phase is difficult as the secondary phases of LaSrGaO4, LaSrGa3O7, La4Ga2O9, and/or LaGa2O4 form readily (Fig. 21) [96, 110]. It is also 2–5 × more expensive than other commercialized electrolytes (Fuelcellmaterials, USA). While the structural stability of LSGM is reported, its reactivity with the common nickel-cermet anodes is undesirable and limits its use as a SOFC electrolyte [111].
Apatite-type structure electrolytes
The apatite structure is described by the general formula A10(MO4)6O2+δ where the A-site is occupied by alkaline/rare earth metals and MO4 is a trivalent anionic group (Fig. 16) [112]. Unlike traditional oxide-ion conductors which conduct through oxygen vacancies, apatite-type materials conduct through interstitial oxygens [112, 113]. Fully stoichiometric apatite materials are poor oxide conductors; by creating excess oxygen or cation vacancies in the structure, the ionic conductivity can be increased by 2 orders of magnitude and 3 orders of magnitude respectively [114]. Thus, cation vacancies are shown to be the most important factor for the oxide conductivity in apatite-type materials. The La10-x(Ge5.5Al0.5O24)O2.75−1.5× series has been shown to have comparable or higher ionic conductivity at ITs compared to YSZ with the x = 0.5 member showing the highest ionic conductivity of 0.16 S/cm at 800 °C (Fig. 22) [98]. However, prolonged heating at temperatures > 1350 °C results in GeO2 leaching out from the structure, lowering the ionic conductivity and limiting its compatibility to only electrodes that sinter/adhere at lower temperatures [115, 116].
Interconnect materials
As a single SOFC is only capable of producing a theoretical voltage of 1.23 V with maximum power occurring at ~ 0.55 V, several SOFCs must be connected in a “stack” which utilizes interconnects to join the anode of a single cell to the cathode of another cell (Fig. 23) [117, 118]. The interconnects function is to separate the cathode oxidizing environment of one cell from the anode reducing environment of another cell while allowing electrons to flow between the two cells [119]. They should meet the following criteria [120, 121]: (i) Under SOFC operating conditions, interconnects must be purely electronic conductors with a minimum electrical conductivity of 1 S/cm and ASR of 0.1 Ω cm2 to minimize the voltage losses due to the interconnect [122, 123]. (ii) Chemical and mechanical stability under SOFC operating conditions and in reducing/oxidizing environments. (iii) TEC match with the anode, cathode, and electrolyte. (iv) No permeability towards oxygen or hydrogen to avoid direct combination and lowering of the cell potential. Interconnect materials for SOFC that can meet these criteria are either metal or ceramic interconnects.
Ceramic interconnects
Lanthanum chromate (LaCrO3) and its doped alternatives are the most widely studied ceramic interconnect for SOFC owing to its moderate electrical conductivity under SOFC conditions, moderate stability in reducing and oxidizing environments, and compatibility with common SOFC materials [121, 125,126,127]. Undoped LaCrO3 conducts electrons through electron holes (h•) formed in the structure to compensate for cation vacancies (\({V}_{La}^{{\prime}{\prime}{\prime}}+{V}_{Cr}^{{\prime}{\prime}{\prime}}\)) according to the reaction [121]:
Due to the dependence of the oxygen partial pressure on conductivity, the LaCrO3 conductivity at the anode side of the cell is low, rendering it unsuitable for use as an SOFC interconnect [128]. At 800 °C, LaCrO3 has a conductivity of 0.96 S/cm and 0.26 S/cm in air and 10%H2/90%N2 respectively (Fig. 24) [129]. However, this can be improved by doping alkaline earth elements (Ca, Sr, and Ba) at the A-site. Both La0.75Sr0.25CrO3 and La0.7Ca0.3CrO3 have a conductivity in oxidizing and reducing environments that is 2 orders of magnitude larger than that of LaCrO3 [129]. While Ba or Mg doping does increase the conductivity, the large size mismatch between La and Ba/Mg causes spinel phases to form which lower the conductivity due to electron-scattering [129, 130].
Metal interconnects
Under high temperature (> 800 °C) and SOFC operating conditions, metallic interconnects will oxidize losing mechanical strength and electronic conductivity with time [131]. However at ITs, metallic interconnects have superior strength and conductivity when compared to ceramic interconnects [119]. Cr/Al is added to Fe/Ni alloys to provide oxidative resistance by forming Cr2O3 and Al2O3 protective layers (Figs. 25 and 26) [132, 133].
Reactive elements with a higher affinity towards oxygen than Cr will enhance the selective oxidation of Cr and suppress outward Cr diffusion reducing the growth rate of Cr2O3 (which leads to layer separation) caused when outward diffusing Cr reactions with inward diffusing oxygen; Al possesses the same properties but to a much lesser extent (Fig. 27) [136].
Al2O3 is not an electronic conductor like Cr2O3 so the Al content must be kept low to avoid forming a continuous insulating oxide layer [137, 138]. For Ni or Fe-based alloys, the addition of a maximum of 3 wt% Al is shown to lower the oxidation rate without the formation of an insulating Al2O3 layer [139]. A major problem with Cr-containing alloys is the Cr-poisoning of the cathode which increases the surface diffusion of oxygen and charge transfer resistance at the TPB [140, 141]. The mechanism for Cr-deposition at the cathode is best described using generalized nucleation deposition theory:
where Na is the nucleation site (e.g., Mn, Sr, Ba, or Co) in the cathode or electrolyte, CrO3(g) is vaporized Cr from the interconnect, and Cr–N-O(nuclei) is the nuclei formed during the nucleation reaction [142, 143]. Cr–N-O(nuclei) will further react with CrO3(g) and deposit Cr in the form of Cr2O3(s) and spinel-based (Cr,Mn)3O4, SrCrO4, BaCrO4, and CoCr2O4 for Mn, Sr, Ba, and Co respectively.
Solid oxide fuel cell efficiency
How is the Nernst potential of a solid oxide fuel cell influenced by gas pressure?
As SOFCs operate at elevated temperature and pressure (non-standard conditions), the Nernst equation is used to calculate the cell’s potential at various temperatures and pressures. The Nernst equation (Eq. 5) relates the cell’s potential (E) to its standard redox potential (1.229 V), the gas constant (R), temperature (T), the number of electrons transferred (z), Faraday’s constant (F), and the partial pressures of water (PH2O), O2 (PO2), and H2 (PH2).
Using this formula, the effect of different gas environments on the Nernst potential can be predicted by keeping the temperature constant and assuming that PO2 or PH2 can change independently of PH2O to isolate these three variables.
In case one, a cell using air (PO2 = 2.1 bar) as an oxygen source for the cathode is fitted with a pure oxygen tank (PO2 = 10 bar). This change is predicted to increase the Nernst potential by 30 mV; however, this small increase in potential may not justify the energy required to obtain pure oxygen [144]. In case two, the hydrogen supplied to the anode is hydrated (97% H2 + 3% H2O) to reduce the dual atmosphere effect [145, 146]. By hydrating the hydrogen, the PH2 decreases from 10 to 9.7 bar which decreases the Nernst potential by 1.1 mV. In this case, hydrating the hydrogen will improve the lifespan of the working SOFC with minimal voltage losses.
What is the thermodynamic efficiency of a solid oxide fuel cell?
Energy conversion efficiency is described as the ratio between output energy over input energy. For an ideal solid oxide fuel cell, the input energy is the enthalpy of reaction for the water formation reaction \(\left(\Delta {\rm H}_{f,{H}_{2}O}\right)\) while the output energy is the \(\Delta {\rm H}_{f,{H}_{2}O}\) subtracted by the energy losses \(\left(\Delta {S}_{{H}_{f,{H}_{2}O}}\right)\) per unit temperature (T) (Eq. (6) [147]. These energy losses include activation, ohmic, and concentration losses [148, 149]. While Eq. 6 shows that the efficiency decreases with increasing temperature, in working SOFCs, this is not the case. The activation, ohmic, and heat transfer losses become significant in SOFCs operating at temperatures below 600 °C which causes ΔS to become much larger than T, greatly lowering the efficiency of the cell at low temperatures [149,150,151].
What is the fuel efficiency of a solid oxide fuel cell?
The fuel utilization of a theoretical SOFC is the ratio between the moles of electrons produced per second (νcharge) and the moles of fuel supplied per second (νfuel) (Eq. 7).
The νcharge of a SOFC is the current density (i), divided by the charge produced by the reaction (zF) where z is the number of electrons produced by the reaction and F is Faraday’s constant. The νfuel is the volumetric flow rate (Q) converted to molar flow rate using the density (ρ) and molar mass (M) of the fuel. Thus, the fuel utilization for a fuel cell is given by Eq. 8.
At maximum fuel efficiency, the hydrogen pressure at the anode will drop to nearly 0. The anode is at risk for reoxidation if the oxygen partial pressure (due to steam) is larger than the hydrogen partial pressure [152, 153]. During reoxidation, the anode will expand and crack (Fig. 28); this behavior is heavily reported for Ni-anodes [154,155,156,157]. Thus, fuel efficiency is kept at ~ 75% to maintain the reducing environment at the anode [158].
Hydrogen recovery is often used in SOFCs due to the simplicity of separating steam from gases. One method is to create a dead-end loop at the anode such that the outlet is sealed so all of the supplied hydrogen is utilized [160]. These systems must be pressure controlled to maintain a higher hydrogen pressure compared to steam to avoid anode reoxidation. While keeping the anode under constant pressure, steam is expelled through a condenser while the total pressure is maintained by flowing hydrogen into the system [161]. A second method is to recirculate the anode off gas back into the fuel stream using a pump/blower and a condenser to remove the steam [162, 163]. The dead-end loop consumes no energy but is unsuitable for high-power SOFCs with rapid fuel consumption; pumps can recirculate at high pressure but oil-lubrication of mechanical parts can contaminate the fuel being recirculated and oil-free pumps face durability problems; and blowers can recirculate large volumes of gas but at low pressure [163, 164].
What is the voltaic efficiency of a solid oxide fuel cell?
The Nernst potential (Eq. 5) of a SOFC is the open-circuit voltage (OCV) assuming complete reversibility of all electrochemical processes within the cell. When drawing current from the SOFC, the cell potential will drop due to overpotential losses [149]. The voltaic efficiency is the ratio between the output cell potential and the Nernst potential (Eq. 9) [165].
The activation overpotential is the potential required to overcome the activation barrier of the cell; this is related to the charge transfer and gas adsorption/desorption on the electrode surface [166]. For purely electronic conducting electrodes where the TPB exists only at the electrode–electrolyte interface, the activation overpotential (ηact) is quantified by Eq. 10 where i is the operating current density of the cell and io,a and io,c are the exchange current densities of the anode and cathode respectively [167, 168]. The hyperbolic sine approximation was used over the Butler-Volmer equation due to its computational simplicity with nearly identical results (Fig. 29).
The ohmic overpotential (ηohm) is the potential required to overcome the internal resistance of the cell [169]. It is quantified by Ohm’s law where i is the operating current density of the cell, Rp is polarization the resistance of the electrodes, and Rs is the series resistance at the electrolyte (Eq. 11) [149].
The concentration overpotential (ηconc) is the potential lost due to the gas concentration gradient between the inlet and the TPB of the porous electrodes [170]. It results from fast electrochemical reactions coupled with slow gas diffusion within the porous electrodes most often occurring at high current [166]. ηconc is quantified using Eq. 12 where P is the pressure of the gas at the inlet/electrode surface and PTPB is the pressure of the gas at the TPB [171].
For purely electronic conducting electrodes where the TPB exists only at the electrode–electrolyte interface, PH2(TPB) and PH2O(TPB) (atm) are related to the total H2 (PH2) and H2O (PH2O) (atm) pressure respectively, the current density of the cell (i (A/cm2)), the length of the anode diffusion path (Lanode (cm)) which is assumed to be the thickness of the anode, and the effective diffusion of the anode (Deff,anode (cm2/s)) (Eqs. 13 and 14); PO2(TPB) is related to total pressure at the cathode (Pc (atm)), the total pressure of O2 (PO2 (atm)), the length of the cathode diffusion path (Lcathode (cm)) which is assumed to be the thickness of the cathode, and the effective diffusion of the cathode (Deff,cathode (cm2/s)) (Eq. 15) [149, 167, 172].
The effective diffusion of binary gases through a porous electrode (Deff (cm2/s)) in SOFCs is modeled using binary diffusion (Dij (cm2/s)) involving the interaction of gas species i and j where T is temperature (K), P is the total pressure (atm), V is the Fuller diffusion volume (cm3/mol) (7.07 for H2, 17.9 for N2, 16.6 for O2, and 12.7 for H2O), M is the molar mass of the gas (g/mol), and 10−3 is an arbitrary constant from the least squares fitting; and the Knudsen diffusion (Dik (cm2/s)) involving the interaction of gas species i with the walls of the porous structure where dp is the mean pore diameter (cm) ((Eq. 16) [173,174,175,176].
Combining Eqs. 12–16 gives the formula for concentration overpotential for SOFCs using experimentally measurable variables (Eq. 17).
Combining Eqs. 5, 9–11, and 17 gives the equation for the voltaic efficiency (εvolt) of a SOFC. Figure 30 shows the influence of hydrogen (PH2) and water (PH2O) partial pressure on εvolt. Since water is a product of the reaction, Le Chatelier’s principle and the Nernst equation predict that a lower PH2O will increase the voltage/rate of reaction for the cell. However, Fig. 30 shows that a PH2O < 0.5 atm (at the conditions listed in Table 4) will greatly lower the εvolt with an exponential decrease in εvolt at PH2O < 1.5 atm; a PH2O > 1.5 atm will linearly decrease εvolt but at a very minimal rate. There is an exponential drop in εvolt at PH2 < 1 atm with a more linear increase in εvolt above 1 atm; εvolt will continue to increase linearly upon increasing PH2.
Solid oxide fuel cell applications
Residential cogeneration
In an ideal SOFC, all the chemical energy present in the feed gases will be converted to electrical energy. However, during operation, some chemical energy is converted to thermal energy mainly due to Joule heating and heat generated by the electrochemical reactions where the HOR is slightly endothermic and the ORR is largely exothermic making the net reaction exothermic [180,181,182]. The high operating temperature and waste heat produced by the SOFC creates high-temperature exhaust gas which can be utilized for residential/commercial heating. Given natural gas is a primary fuel for residential and commercial heating, many cities have established pipelines to directly supply buildings with natural gas [183]. With the infrastructure already in place, SOFC units can be installed in buildings for dual power and heating. One of the most successful examples of this is the joint development between Osaka Gas, Kyocera, Toyota Motor, and Aisin on the ENE-FARM type S. The Osaka Gas and Kyocera SOFC system showed 45% chemical-to-electrical energy conversion, 30% chemical-to-thermal energy conversion, and 15% of the energy was lost [184]. Over each year, the electrical efficiency of the ENE-FARM type S was improved by thinning the electrolyte, electrodepositing (Zn, Mn, Co)3O4 on the stainless steel interconnects, improving the airflow, enhancing the thermal insulation, and improving the accuracy of fuel delivery [185, 186]. One of the ENE-FARM type s’s deployed in 2009 has achieved over 10 years of operation with only a 5% drop in chemical-to-electrical energy conversion efficiency (Fig. 31) [187]. The 2016 model features a 0.3 m3, 106 kg SOFC/hot water storage tank connected to a 0.1 m3, 38 kg hot water unit. It has an estimated lifespan of 10 years and can output a maximum of 700 W (enough to sustain the average home energy demand) with a chemical-to-electrical conversion efficiency of 52%; 35% of the electrical losses are in the form of thermal energy used to heat the hot water unit and the remaining 13% are losses [185].
Automotive
In 2016, Nissan Motor Co. unveiled the world’s first SOFC-powered vehicle prototype capable of reaching over 600 km on a 30-L bio-ethanol tank [188]. However, electrode or electrolyte-supported cells made of ceramics are damaged upon rapid heating due to poor thermal shock resistance and require slow heating to reach the operating temperature [189]. The slow startup of these cell designs will not work for automotive purposes where the SOFC will need to be quickly heated and cycled between room and operating temperature. By adding a metal support layer (MS), typically composed of ferric stainless steel, cells can withstand larger temperature gradients and faster thermal cycling [190,191,192]. UK based, Ceres Power has partnered with Bosch, Nissan, and Weichai Power to commercialize MS-SOFCs [193]. Utilizing the Ceres SteelCell® technology, Weichai commercialized the world’s first high-power MS-SOFC running on biomass gas and H2 with a chemical-to-electrical conversion efficiency of > 60%, chemical-to-thermal conversion efficiency of 32.55%, with the remaining 7.45% being losses [194, 195]. The potential for these SOFCs to be utilized in vehicles was seen by Nissan and 2018, partnering with Ceres Power and The Welding Institute to develop electric vehicles equipped with SOFCs as range extenders [196].
Conclusions
SOFCs operating with hydrogen as a fuel are a promising source of carbon–neutral energy that uses a chemical-to-electrical energy conversion process to convert oxygen and hydrogen into electricity and water. For IT-SOFC, the cathode must have high catalytic activity towards the ORR (ASR < 0.1 Ω cm2), MIEC (> 100 S/cm), compatibility with electrolyte and interconnect materials, and structural stability under SOFC operating conditions. SOFC cathodes typically have a perovskite, layered-perovskite, or double-perovskite type-structure with perovskite-type structures being more widely used/studied due to their higher stability and conductivity. At ITs, the anode must have high catalytic activity towards the HOR (ASR < 0.1 Ω cm2), MIEC (> 100 S/cm), compatibility with electrolyte and interconnect materials, and structural stability under SOFC operating conditions. SOFC anodes are typically Ni-cermet, Cu-cermet, or perovskite-type anodes with Ni-cermet anodes being more widely used/studied due to their superior conductivity, HOR activity, and stability. At ITs, the electrolyte must have high oxide ion conductivity (> 0.1 S/cm) with minimal electronic conductivity (~ 0 S/cm), structural stability under SOFC operating conditions, and compatibility with electrode and interconnect materials. SOFC electrolytes are typically fluorite, perovskite, or apatite-type electrolytes with fluorite-type materials being more popular due to their higher structural stability; perovskite-type electrolytes have been shown to have higher ionic conductivity at lower temperatures than fluorite-type materials but are more reactive and have a larger manufacturing/material cost. At SOFC conditions, the interconnect must be a purely electronic conductor (> 1 S/cm), have a low ASR (< 0.1 Ω cm2), stable in reducing and oxidizing environments, have a TEC match with the electrodes and electrolyte, and have no permeability towards oxygen or hydrogen. SOFC interconnects are either ceramic or metal-based with metal-based interconnects being more widely used due to their higher electronic conductivity and lower hydrogen/oxygen permeability.
SOFC efficiency is separated into three components: thermodynamic, fuel, and voltaic efficiency. The thermodynamic efficiency is the ratio between the output energy (ΔG) and the input energy (ΔH). The fuel efficiency is the ratio between the moles of electrons generated and the moles of fuel supplied; fuel efficiency can be increased using fuel recovery techniques. The voltaic efficiency is the ratio between the operating cell potential (Nernst potential minus the activation, ohmic, and concentration overpotential) and the Nernst potential. It is found that the voltaic efficiency exponentially decreases when PH2O and PH2 < PO2 and linearly increases with PH2O and PH2.
The high operating temperature of SOFCs produces high-temperature exhaust gas making SOFCs an appealing option for sectors in need of combined heat and power. Many American states such as Utah and California as well as Canadian provinces such as Alberta or Saskatchewan already supply a large percentage of homes with natural gas for heating; with the infrastructure already in place, the transition towards residential sectors being powered by SOFCs is a realistic goal for the near future. This concept has been successfully deployed in Japan with the ENE-FARM type S being sold and installed since 2020. To make this technology cleaner, homes should be equipped with carbon capture technology to avoid the CO2 emissions when utilizing natural gas as a fuel or homes should be directly supplied with hydrogen.
Data availability
No datasets were generated or analyzed during the current study.
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Acknowledgements
The Natural Sciences and Engineering Research Council of Canada (NSERC) have supported this work through discovery grants to one of us (Venkataraman Thangadurai) (Award number: RGPIN-2021-02493). V.T. thanks the University of St Andrews for their recent employment as Chair in Energy. Dr. Thangadurai would like to dedicate this article to Prof. Ashok Kumar Shukla’s virtual issue in honor of his contribution to electrochemistry.
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Sikstrom, D., Thangadurai, V. A tutorial review on solid oxide fuel cells: fundamentals, materials, and applications. Ionics (2024). https://doi.org/10.1007/s11581-024-05824-7
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DOI: https://doi.org/10.1007/s11581-024-05824-7